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Exact Recursive probabilistic programming

PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2023年第OOPSLA期7卷 665-695页

作者： Chiang, David McDonald, Colin Shan, Chung-chieh Univ Notre Dame Dept Comp Sci & Engn Notre Dame IN 46556 USA Indiana Univ Dept Comp Sci Bloomington IN USA

Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also useful, but unfortunately, existing probabilistic programming languages do not perform exact inference on recursive calls over recursive data, forcing programmers to code many applications manually. We introduce a probabilistic language in which a wide variety of recursion can be expressed naturally, and inference carried out exactly. For instance, probabilistic pushdown automata and their generalizations are easy to express, and polynomial-time parsing algorithms for them are derived automatically. We eliminate recursive data types using program transformations related to defunctionalization and refunctionalization. These transformations are assured correct by a linear type system, and a successful choice of transformations, if there is one, is guaranteed to be found by a greedy algorithm.

关键词： probabilistic programming recursive types linear types

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Concavity and efficient points of discrete distributions in probabilistic programming

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MATHEMATICAL programming 2000年第1期89卷 55-77页

作者： Dentcheva, D Prékopa, A Ruszczynski, A Stevens Inst Technol Dept Math Sci Hoboken NJ 07030 USA RUTCOR Piscataway NJ 08854 USA Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08854 USA

We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal Value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.

关键词： probabilistic programming discrete distributions generalized concavity column generation

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Bayesian Modelling of Student Misconceptions in the one-digit Multiplication with probabilistic programming 16

Bayesian Modelling of Student Misconceptions in the one-digi...

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6th International Conference on Learning Analytics and Knowledge (LAK)

作者： Taraghi, Behnam Saranti, Anna Legenstein, Robert Ebner, Martin Graz Univ Technol Educ Technol Munzgrabenstr 35 A-8010 Graz Austria Graz Univ Technol Inst Theoret Comp Sci Inffeldgasse 16b-1 A-8010 Graz Austria

ISBN: (纸本)9781450341905

One-digit multiplication errors are one of the most extensively analysed mathematical problems. Research work primarily emphasises the use of statistics whereas learning analytics can go one step further and use machine learning techniques to model simple learning misconceptions. probabilistic programming techniques ease the development of probabilistic graphical models (bayesian networks) and their use for prediction of student behaviour that can ultimately influence learning decision processes.

关键词： Learning Analytics Bayesian Modelling probabilistic programming One-Digit Multiplication

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A Design Proposal for Gen: probabilistic programming with Fast Custom Inference via Code Generation 2

A Design Proposal for Gen: Probabilistic Programming with Fa...

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2nd ACM SIGPLAN InternationalWorkshop on Machine Learning and programming Languages (MAPL)

作者： Cusumano-Towner, Marco Mansinghka, Vikash K. MIT Probabilist Comp Project 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781450358347

probabilistic programming languages have the potential to make probabilistic modeling and inference easier to use in practice, but only if inference is sufficiently fast and accurate for real applications. Thus far, this has only been possible for domain-specific languages that focus on a restricted class of models and inference algorithms. This paper proposes a design for a probabilistic programming language called Gen, embedded in Julia, that aims to be sufficiently expressive and performant for general-purpose use. The language provides constructs for automatically generating optimized implementations of custom inference tactics based on static analysis of the target probabilistic model. This paper informally describes a language design for Gen, and shows that Gen is more expressive than Stan, a widely used language for hierarchical Bayesian modeling. A first benchmark shows that a prototype implementation of Gen can be as fast as Stan, only similar to 1.4x slower than a hand-coded sampler in Julia, and similar to 7,500x faster than Venture, one of the only other probabilistic languages with support for custom inference.

关键词： probabilistic programming static analysis code generation custom inference inference tactics

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Solving probabilistic programming problems involving multi-choice parameters

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OPSEARCH 2011年第3期48卷 217-235页

作者： Acharya, Srikumar Biswal, Mahendra Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

probabilistic programming is used in some optimization problems where some or all parameters are considered as random variables, in order to deal with uncertainty, which is an inherent feature of the system. The situation of multiple parameters may exist in a decision making problem in our real life. The multi-choice programming can not only avoid the underestimation of parameters, but also can decide the appropriate parameter from multiple parameters. This paper deals with a probabilistic linear programming problem, where the right hand side parameters of probabilistic constraints are multichoice in nature and rest of the parameters are independent random variables. In this paper the probabilistic programming problem is converted to an equivalent deterministic mathematical programming model. The resulting model is then solved by standard linear or non-linear programming techniques. A numerical example is presented to illustrate the methodology.

关键词： probabilistic programming Multi-choice programming Non-linear programming Normal distribution

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Fabular: Regression Formulas as probabilistic programming 16

Fabular: Regression Formulas as Probabilistic Programming

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43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of programming Languages (POPL)

作者： Borgstrom, Johannes Gordon, Andrew D. Ouyang, Long Russo, Claudio Scibior, Adam Szymczak, Marcin Uppsala Univ S-75105 Uppsala Sweden Microsoft Res Bangalore Karnataka India Univ Edinburgh Edinburgh EH8 9YL Midlothian Scotland Stanford Univ Stanford CA 94305 USA Univ Cambridge Cambridge CB2 1TN England MPI Tubingen Tubingen Germany

ISBN: (纸本)9781450335492

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.

关键词： Bayesian inference linear regression probabilistic programming relational data hierarchical models

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A Live, Multiple-Representation probabilistic programming Environment for Novices 16

A Live, Multiple-Representation Probabilistic Programming En...

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34th Annual CHI Conference on Human Factors in Computing Systems (CHI4GOOD)

作者： Gorinova, Maria I. Sarkar, Advait Blackwell, Alan F. Syme, Don Univ Cambridge Comp Lab 15 JJ Thomson Ave Cambridge England Microsoft Res Cambridge Cambridge England

ISBN: (纸本)9781450333627

We present a live, multiple-representation novice environment for probabilistic programming based on the Infer. NET language. When compared to a text-only editor in a controlled experiment on 16 participants, our system showed a significant reduction in keystrokes during introductory probabilistic programming exercises, and subsequently, a significant improvement in program description and debugging tasks as measured by task time, keystrokes and deletions.

关键词： probabilistic programming visual languages multiple representation computational thinking development environment

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Fast and Correct Gradient-Based Optimisation for probabilistic programming via Smoothing 1

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32nd European Symposium on programming (ESOP) Held as Part of the 26th European Joint Conferences on Theory and Practice of Software (ETAPS)

作者： Khajwal, Basim Ong, C-H Luke Wagner, Dominik Univ Oxford Oxford England Nanyang Technol Univ Singapore Singapore

ISBN: (数字)9783031300448

ISBN: (纸本)9783031300431;9783031300448

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular, a variant using the so-called reparameterisation gradient estimator exhibits fast convergence in a traditional statistics setting. Unfortunately, discontinuities, which are readily expressible in programming languages, can compromise the correctness of this approach. We consider a simple (higher-order, probabilistic) programming language with conditionals, and we endow our language with both a measurable and a smoothed (approximate) value semantics. We present type systems which establish technical pre-conditions. Thus we can prove stochastic gradient descent with the reparameterisation gradient estimator to be correct when applied to the smoothed problem. Besides, we can solve the original problem up to any error tolerance by choosing an accuracy coefficient suitably. Empirically we demonstrate that our approach has a similar convergence as a key competitor, but is simpler, faster, and attains orders of magnitude reduction in work-normalised variance.

关键词： probabilistic programming variational inference reparameterisation gradient value semantics type systems.

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HackPPL: A Universal probabilistic programming Language 3

HackPPL: A Universal Probabilistic Programming Language

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3rd ACM SIGPLAN International Workshop on Machine Learning and programming Languages (MAPL)

作者： Ai, Jessica Arora, Nimar S. Dong, Ning Gokkaya, Beliz Jiang, Thomas Kubendran, Anitha Kumar, Arun Tingley, Michael Torabi, Narjes Facebook Inc Menlo Pk CA 94025 USA

ISBN: (纸本)9781450367196

HackPPL is a probabilistic programming language (PPL) built within the Hack programming language. Its universal inference engine allows developers to perform inference across a diverse set of models expressible in arbitrary Hack code. Through language-level extensions and direct integration with developer tools, HackPPL aims to bridge the gap between domain-specific and embedded PPLs. This paper overviews the design and implementation choices for the HackPPL toolchain and presents findings by applying it to a representative problem faced by social media companies.

关键词： probabilistic programming probabilistic Representations Hack Coroutines Bayesian Inference Markov-chain Monte Carlo methods Variational methods Social Networks Crowd-sourcing

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Practical probabilistic programming

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20th International Conference on Inductive Logic programming (ILP)

作者： Pfeffer, Avi Charles River Analyt Cambridge MA 02140 USA

ISBN: (纸本)9783642212949;9783642212956

probabilistic programming promises to make probabilistic modeling easier by making it possible to create models using the power of programming languages, and by applying general-purpose algorithms to reason about models. We present a new probabilistic programming language named Figaro that was designed with practicality and usability in mind. Figaro can represent models naturally that have been difficult to represent in other languages, such as probabilistic relational models and models with undirected relationships with arbitrary constraints. An important feature is that the Figaro language and reasoning algorithms are embedded as a library in Scala. We illustrate the use of Figaro through a case study.

关键词： probabilistic modeling representation languages probabilistic programming

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